<div class="problemindexholder" problemindex="B">
 <div class="ttypography">
  <div class="problem-statement">
   <div class="header">
    <div class="title">
     B. Volatile Kite
    </div>
    <div class="time-limit">
     <div class="property-title">
      time limit per test
     </div>
     2 seconds
    </div>
    <div class="memory-limit">
     <div class="property-title">
      memory limit per test
     </div>
     256 megabytes
    </div>
    <div class="input-file">
     <div class="property-title">
      input
     </div>
     standard input
    </div>
    <div class="output-file">
     <div class="property-title">
      output
     </div>
     standard output
    </div>
   </div>
   <div>
    <p>
     You are given a convex polygon
     <span class="tex-span">
      <i>
       P
      </i>
     </span>
     with
     <span class="tex-span">
      <i>
       n
      </i>
     </span>
     distinct vertices
     <span class="tex-span">
      <i>
       p
      </i>
      <sub class="lower-index">
       1
      </sub>
      ,
      <i>
       p
      </i>
      <sub class="lower-index">
       2
      </sub>
      , ...,
      <i>
       p
      </i>
      <sub class="lower-index">
       <i>
        n
       </i>
      </sub>
     </span>
     . Vertex
     <span class="tex-span">
      <i>
       p
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
     </span>
     has coordinates
     <span class="tex-span">
      (
      <i>
       x
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      ,
      <i>
       y
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      )
     </span>
     in the 2D plane. These vertices are listed in clockwise order.
    </p>
    <p>
     You can choose a real number
     <span class="tex-span">
      <i>
       D
      </i>
     </span>
     and move each vertex of the polygon a distance of at most
     <span class="tex-span">
      <i>
       D
      </i>
     </span>
     from their original positions.
    </p>
    <p>
     Find the maximum value of
     <span class="tex-span">
      <i>
       D
      </i>
     </span>
     such that no matter how you move the vertices, the polygon does not intersect itself and stays convex.
    </p>
   </div>
   <div class="input-specification">
    <div class="section-title">
     Input
    </div>
    <p>
     The first line has one integer
     <span class="tex-span">
      <i>
       n
      </i>
     </span>
     (
     <span class="tex-span">
      4 ≤
      <i>
       n
      </i>
      ≤ 1 000
     </span>
     ) — the number of vertices.
    </p>
    <p>
     The next
     <span class="tex-span">
      <i>
       n
      </i>
     </span>
     lines contain the coordinates of the vertices. Line
     <span class="tex-span">
      <i>
       i
      </i>
     </span>
     contains two integers
     <span class="tex-span">
      <i>
       x
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
     </span>
     and
     <span class="tex-span">
      <i>
       y
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
     </span>
     (
     <span class="tex-span">
      - 10
      <sup class="upper-index">
       9
      </sup>
      ≤
      <i>
       x
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      ,
      <i>
       y
      </i>
      <sub class="lower-index">
       <i>
        i
       </i>
      </sub>
      ≤ 10
      <sup class="upper-index">
       9
      </sup>
     </span>
     ) — the coordinates of the
     <span class="tex-span">
      <i>
       i
      </i>
     </span>
     -th vertex. These points are guaranteed to be given in clockwise order, and will form a strictly convex polygon (in particular, no three consecutive points lie on the same straight line).
    </p>
   </div>
   <div class="output-specification">
    <div class="section-title">
     Output
    </div>
    <p>
     Print one real number
     <span class="tex-span">
      <i>
       D
      </i>
     </span>
     , which is the maximum real number such that no matter how you move the vertices, the polygon stays convex.
    </p>
    <p>
     Your answer will be considered correct if its absolute or relative error does not exceed
     <span class="tex-span">
      10
      <sup class="upper-index">
       - 6
      </sup>
     </span>
     .
    </p>
    <p>
     Namely, let's assume that your answer is
     <span class="tex-span">
      <i>
       a
      </i>
     </span>
     and the answer of the jury is
     <span class="tex-span">
      <i>
       b
      </i>
     </span>
     . The checker program will consider your answer correct if
     <img align="middle" class="tex-formula" src="/predownloaded/c6/2e/c62ea64d4651240724c5ac4779b671c741edec24.png" style="max-width: 100.0%;max-height: 100.0%;"/>
     .
    </p>
   </div>
   <div class="sample-tests">
    <div class="section-title">
     Examples
    </div>
    <div class="sample-test">
     <div class="input">
      <div class="title">
       Input
      </div>
      <pre>4<br/>0 0<br/>0 1<br/>1 1<br/>1 0<br/></pre>
     </div>
     <div class="output">
      <div class="title">
       Output
      </div>
      <pre>0.3535533906<br/></pre>
     </div>
     <div class="input">
      <div class="title">
       Input
      </div>
      <pre>6<br/>5 0<br/>10 0<br/>12 -4<br/>10 -8<br/>5 -8<br/>3 -4<br/></pre>
     </div>
     <div class="output">
      <div class="title">
       Output
      </div>
      <pre>1.0000000000<br/></pre>
     </div>
    </div>
   </div>
   <div class="note">
    <div class="section-title">
     Note
    </div>
    <p>
     Here is a picture of the first sample
    </p>
    <p>
     <img class="tex-graphics" src="/predownloaded/8f/73/8f737928ca9f81d14c2a5e67deaf40a3d3bdfe62.png" style="max-width: 100.0%;max-height: 100.0%;"/>
    </p>
    <p>
     Here is an example of making the polygon non-convex.
    </p>
    <p>
     <img class="tex-graphics" src="/predownloaded/21/1b/211b430e19e6c6407693098952b6d4e04638b0fa.png" style="max-width: 100.0%;max-height: 100.0%;"/>
    </p>
    <p>
     This is not an optimal solution, since the maximum distance we moved one point is
     <span class="tex-span">
      ≈ 0.4242640687
     </span>
     , whereas we can make it non-convex by only moving each point a distance of at most
     <span class="tex-span">
      ≈ 0.3535533906
     </span>
     .
    </p>
   </div>
  </div>
  <p>
  </p>
 </div>
</div>
